Similarities of discrete and continuous Sturm-Liouville problems
Date
2007-12-06
Authors
Ghanbari, Kazem
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
Abstract
In this paper we present a study on the analogous properties of discrete and continuous Sturm-Liouville problems arising in matrix analysis and differential equations, respectively. Green's functions in both cases have analogous expressions in terms of the spectral data. Most of the results associated to inverse problems in both cases are identical. In particular, in both cases Weyl's m-function determines the Sturm-Liouville operators uniquely. Moreover, the well known Rayleigh-Ritz Theorem in linear algebra can be proved by using the concept of Green's function in discrete case.
Description
Keywords
Green's function, Jacobi matrix, Sturm-Liouville equation, Eigenvalue, Eigenvector
Citation
Ghanbari, K. (2007). Similarities of discrete and continuous Sturm-Liouville problems. <i>Electronic Journal of Differential Equations, 2007</i>(172), pp. 1-8.
Rights
Attribution 4.0 International